Least Common Multiple (LCM) of 80 and 182
The least common multiple (LCM) of 80 and 182 is 7280.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 80 and 182?
First, calculate the GCD of 80 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 182 = 0 remainder 80 |
| 2 | 182 ÷ 80 = 2 remainder 22 |
| 3 | 80 ÷ 22 = 3 remainder 14 |
| 4 | 22 ÷ 14 = 1 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 20 | 3580 |
| 159 and 107 | 17013 |
| 136 and 80 | 1360 |
| 14 and 142 | 994 |
| 20 and 200 | 200 |